Molecular modelling Hartree-Fock

DFT methods are attractive because they include the effects of electron correlation—the fact that electrons in a molecular system react to one another s motion and attempt to keep out of one another s way—in their model. Hartree-Fock calculations consider this effect only in an average sense—each electron sees and... 

Relative times for the MMFF molecular mechanics model, the AMI semi-empirical model, Hartree-Fock models with 3-2IG, 6-3IG and 6-311+G basis sets, EDFl and B3LYP density functional models and the MP2 model with 6-3IG and 6-311+G basis sets, for energy calculations, geometry optimizations and frequency evaluations, and the localized MP2 (LMP2) model with 6-3 IG and... 

Size Consistent. Methods for which the total error in the calculated energy is more or less proportional to the (molecular) size. Hartree-Fock and Moller-Plesset models are size consistent, while Density Functional Models, (limited) Configuration Interaction Models and Semi-Empirical Models are not size consistent. 

The second and most important point of Table 3.16 is that the correct Hartree-Fock results are in qualitative disagreement with experiment. In the molecular orbital Hartree-Fock model, the l7r orbital is the highest occupied orbital, yet the lowest experimental ionization potential corresponds to the production of an ion with symmetry. This implies a breakdown of the simple orbital picture of ionization. The Hartree-Fock picture is an approximation. For the case of N2 this approximation is not sufficiently accurate for even a qualitative understanding of the ionization phenomena. As we shall see in Chapters 4 and 7, when the single determinant Hartree-Fock model is replaced by a multideterminantal model, with its associated inclusion of correlation effects, theoretical calculations and experiment ultimately agree on the ionization spectra of N2. 

Mciny of the theories used in molecular modelling involve multiple integrals. Examples include tire two-electron integrals formd in Hartree-Fock theory, and the integral over the piriitii >ns and momenta used to define the partition function, Q. In fact, most of the multiple integrals that have to be evaluated are double integrals. 

As a final note, be aware that Hartree-Fock calculations performed with small basis sets are many times more prone to finding unstable SCF solutions than are larger calculations. Sometimes this is a result of spin contamination in other cases, the neglect of electron correlation is at the root. The same molecular system may or may not lead to an instability when it is modeled with a larger basis set or a more accurate method such as Density Functional Theory. Nevertheless, wavefunctions should still be checked for stability with the SCF=Stable option. ... 

As we have seen throughout this book, the Hartree-Fock method provides a reasonable model for a wide range of problems and molecular systems. However, Hartree-Fock theory also has limitations. They arise principally from the fact that Hartree-Fock theory does not include a full treatment of the effects of electron correlation the energy contributions arising from electrons interacting with one another. For systems and situations where such effects are important, Hartree-Fock results may not be satisfactory. The theory and methodology underlying electron correlation is discussed in Appendix A. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

An Application of the Half-Projected Hartree-Fock Model to the Direct Determination of the Lowest Singlet and Triplet Excited States of Molecular Systems... 

Most semi-empirical models are based on the fundamental equations of Hartree-Fock theory. In the following section, we develop these equations for a molecular system composed of A nuclei and N electrons in the stationary state. Assuming that the atomic nuclei are fixed in space (the Born-Oppenheimer approximation), the electronic wavefunction obeys the time-independent Schrodinger equation ... 

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